Learning Large $Q$-matrix by Restricted Boltzmann Machines

Estimation of the large $Q$-matrix in Cognitive Diagnosis Models (CDMs) with many items and latent attributes from observational data has been a huge challenge due to its high computational cost. Borrowing ideas from deep learning literature, we propose to learn the large $Q$-matrix by Restricted Boltzmann Machines (RBMs) to overcome the computational difficulties. In this paper, key relationships between RBMs and CDMs are identified. Consistent and robust learning of the $Q$-matrix in various CDMs is shown to be valid under certain conditions. Our simulation studies under different CDM settings show that RBMs not only outperform the existing methods in terms of learning speed, but also maintain good recovery accuracy of the $Q$-matrix. In the end, we illustrate the applicability and effectiveness of our method through a real data analysis on the Cattell's 16 personality test data set.